Confinement of CR in Dark Matter relic clumps

Transcription

1 Confinement of CR in Dark Matter relic clumps University Karlsruhe and SINP Moscow State University W.de Boer University Karlsruhe 1

2 Dark Matter in Universe and the Galaxy Strong evidences for DM existence: galactic rotation curves large scale structures nucleosynthesis and element abundances Modern cosmology: inflation scenario Ω~1, Ω λ ~0.73, Ω χ ~0.23 bottom-top scenario P(k)~k n, n>0.95 small structures(clumps) are created first universal DM profile for different scales Cuspy (γ>0) profile from Nbody and analytical simulation (NFW parametrization): Spectrum of structure scales k n DM profiles from Nbody sim. Tegmark et al 2002 Navarro et al

3 Fraction of DM in relic clumps : depends upon; spectrum of primary fluctuations δ k n clumps density profile : ρ~r α, α=1.5-2 r<r c =δ 3 r clump, r c ~ r cl, ρ max -? mass spectrum dn cl and minimum mass M min M min = M is defined by free streaming of DM after decoupling ζ of DM is in relic clumps the rest is the 'bulk' DM Clumps distribution in the Galaxy n cl : DM clumps follows the bulk DM distribution (universal profile) tidal disruption by Galactic potential can disturb the distribution (depletion near the center) large scale structure appears due to 'recent' infalls (CanisM,Sag.) Gurevich et al 1997 Diemand et al 06, Berezinskii et al 03 Dokuchaev et al 03 dn/dm cl Nbody simulations Stoehr et al 2004 Ex. smallest clumps: M=10-8 M, r~100 AU, < ~100 GeV/cm 3, max ~ GeV/cm 3 ~1-100 clumps/pc 3 at R =8.5 kpc, bulk ~ GeV/cm 3 3

4 DM annihilation DM can annihilate (or coannihilate) with the averaged cross section <σν> constrained by relic density in time of decoupling T dec ~m χ /20~3-50 GeV <σν> = cm 3 s -1 / Ω χ h 2 [ ], <σν> cm 3 s -1 The dominant end state are fermions After hadronization and fragmentation stable particles: p, pb, e+, e-, γ Nowadays (T~1.8 K) <σν>can be only smaller Momentum dependency of <σv> for different annihilation channels in SUSY scenario (m GeV) Yields Y i per annihilation SUSY neutralino 60 GeV T now T dec 4 DeBoer et al 2005

5 DM annihilation(dma) in the Galaxy Annihilation signal : q~1/m χ 2-4 DMA signal / CR background for the bulk galactic DM (different profiles and m χ ) Cusped profile r GALPROP+DMA Cored profile (a+r) Zhukov et al q i (r,p)= <σν> Y i (p) ρ2 (x)/m χ 2 dx Experimental resolution (EGRET, Bess, Caprice, etc) ~10% Model uncert. can be much larger.. Boost factor: if relic clumps exist DM annihilation signal Q DMA ~ ρ 2 is dominated by cusp of smallest DM clumps max max ρ tot =ρ bulk +ρ cl, ρ cl >>ρ bulk B= Q, tot /Q bulk, B= max depending on ζ and ρ cl if n cl ~ ρ bulk, B~1/ρ bulk, Q tot ~ ρ -> effective DMA profile instead of DM bulk profile bulk 5

6 Berezynskii et al 1990 CR propagation CR propagation: as a resonant scattering of CR f(r) on MHD turbulences with spectral density W(k,r): 1/k r ~ r g =pc/zeb k~10-12 cm -1 for GeV particles in B~10-6 G Source term for a DM clump 2 q i (r,p)~ <σν> Y i (p) ρ ο2 /m χ diffusion Vc-convection P losses Decays and fragmentation Alfven speed MHD waves interact with CR growth by CR if V str > v a damping Armstrong et al 1995 W(k) is related to the scale of interstellar irregularities, follows W~k a-2, a=1/3 for Kalamogorov spectrum small scales 1/k<10 14 cm are created by CR streaming(?) 6 Scales spectrum in electron density

7 Growth and damping of MHD turbulences Enhancement of the MHD waves by CR streaming: pitch angle scattering µ =cosθ At resonance vµ=ω/k small at E<1 GeV for DMA products Kulsrud 69 Wentzel 1974 Damping: 1. ions -neutral gas friction <n H > ~1 cm -3, <n HI > ~0.01 cm -3 molecular clouds n H ~ cm -3 <σ col v> ~10-9 cm 3 s -1 MHD are damped in the dense gas clouds (galactic disk, clouds) 2. nonlinear damping by MHD waves collisions << S H important in the underdense regions (halo, Local Bubble) Anisotropic term from diffusion equation: (if Vc~0, Ploss~0, no reacc.) damping by CR significant for the Kraichan spectrum, at 1/k<10 13 cm Ptuskin et al

8 Maximum at r max ~ sqrt(g/s H ) MHD waves from DM clumps DM clump is a constant, point like source of CR(p,e) can enhance MHD waves. Steady state solution for W(r) (simplified): CR p (1GeV) + DMA p from a clump at 8kpc W(r) s nl =S n l /v a s H =S H /v a g~< v>y tot max r c /m W(r) dependency for a DM clump W(k) W(k) is cutoff at ~m χ can be extended by cascading eb/m y. kpc x. kpc CR proton density distribution in Galaxy GALPROP Conventional model Assumptions: - spherical symmetry (growth is along B field) - DM clump is point like source ( cusped profile) - f(p)~ const - no losses - Vc~0, small local convection - Va~const, δb/b is small - no interference between electrons and protons... 8 GALPROP+DMA

9 CR confinement in DM clumps Stability conditions of the confinement zone: slow proper motion of clumps V cl < v a large external diffusion D ext >D c (W int >W ext ) slow external convection V c < v a DM clump can create a trapping region with low D c Different environments: molecular gas clouds H2 = cm -3 -strong damping underdense regions (Local Bubble, galactic halo) <0.1cm -3, low W density Nbody sim. Distribution of clumps by proper motion in the Galaxy Moore et al 2002 D ext >>D c τ c ~ r cl 2 / 2D c DMA e, p local variations in diffusion coefficient and therefore CR density f*v str /B ~ const synchrotron D c e DMclump B DMA E~ 0.1 m IC < 1GeV DMA contributions: γ from χχ->ffbar->γ+x γ from DMA e+,e- via IC,Bremss. p+,p-, e+, e- from χχ->ffbar->p,e+x radio from e+,e- synchrotron losses 9

10 Isotropic galactic model Isotropic and uniform propagation model: D- isotropic diffusion and uniform averaged gas density <nh>, no gas clouds Z h ~+-4 kpc LB: D~ cm 2 s V conv < 10 km/s Source(r) n(r,z<100pc)~1cm -3 δ(100 GeV)<10-3 T esc ~ Z h2 /D Use locally measured secondaries to constrain the galactic global parameters (D,Z, Va,Vc) Normalize CR primary density to locally observed at R=8.5 kpc ~ 7 g/cm 2 y. kpc x. kpc CR protons density 1 GeV Fails to explain gamma rays unless proton (e) interstellar spectrum has a strong break at 1-10 GeV Moscalenko, Strong 2004 B/C Be 10 /Be 9 Va~30km/s Conventional Model CM (GALPROP) 10 Variations in gas, sources, ISRF, etc γ rays normalized at 0.1 GeV strong break in p spectrum at 10 GeV Hunter et al 98 M&S 2004

11 Inhomogeneous model: a possibility But propagation is not uniform: DM clumps trapping zones with small D c gas is clumpy, ~50% in H2 clouds cm -3 Local Bubble, underdense regions, large W is possible trapping in magnetic mirrors two zones model, convective halo driven by CR... Z h >+-4 kpc Z d ~100 pc D h <D d V c >Z h2 /D h, D >D z r n H ~0 D d >D c D c n H -clumpy Local CR and DMA fluxes with different D isotropic CM GALPROP z=+-4kpc Propagation in non homogeneous medium: Kulsrud, Pearce 69 Ptuskin, Soutoul, Osborne 90 Zwiebel, Shull 82, Padoan, Scalo 2006 Chandran 2000, etc... Assumptions: Large D d in the gal. disk z d ~100pc Small D h in the halo, large V conv Clumpy zones with local confinement (DM clumps, trapping in clouds, etc) D c Confinement zones with Dc<Dd: increase the grammage X locally (r cl ~10pc, n cl =200 cm -3 ) ~ N cl *10-2 isotropize CR f=fd+fcl CM 11

12 Ex: isotropic propagation model with DMA DeBoer et al 2005 EGRET excess interpreted as a DMA signal (SUSY neutralino) m χ ~ 60 GeV Boost factor ~50 -> DM clumps DMA Reconstruct DMA effective profile (clumps distribution) from angular profiles IC,Bremss. from DMA e Explains rotation curves But too many p - and e + from DMA in isotropic CM DMA antiprotons(1gev) in CM DM rings like structure from 'EGRET' profiles (GALPROP+DMA) 12

13 Ex: DMA in model with inhomogeneous medium Decouples locally observed CR secondaries (B,Be, etc) from charged DMA and gamma rays GALPROP (Moscalenko, Strong) modified: including DMA using 'EGRET' profile, anisotropic nonuniform propagation (AD+DMA) More parameters, more freedom, for.ex: Gamma rays Zd=200 pc D d =10 30 cm 2 s n(r,z), snr(r,z) (Lorimer et al) Zh=4 kpc D h =10 28 cm 2 s, Vc=z*dV/dz=20 km/s/kpc nh2 scaling~40 antiprotons B/C 13

14 Summary Annihilation in cuspy relic DM clumps can produce MHD waves with scales k > eb/m χ and confine charged CR The confinement zones will contribute to small scale variations in propagation parameters. These variations can decouple locally observed fluxes from the galactic averages The confinement zones can isotropize CR and produce secondaries locally thus allowing larger diffusion coefficient in the galactic disk The annihilation signal can be attributed to the gamma rays, antiprotons and positrons. In inhomogeneous medium the DMA charged contributions can be not directly related to the gamma rays from DMA 14